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# OpenCV-Python

### OpenCV Python Tutorials

opencvpython.blogspot.com

## Histograms - 4 : Backprojection

Hi friends,

Today, we will look into histogram back-projection. It was proposed by Michael J. Swain , Dana H. Ballard in their paper "Indexing via color histograms".

Well, what is it actually in simple words? It is used for image segmentation or finding objects of interest in an image. In simple words, it creates an image of the same size (but single channel) as that of our input image, where each pixel corresponds to the probability of that pixel belonging to our object. So in short, the output image will have our object of interest in white and remaining part in black. Well, that is an intuitive explanation.

(In this article, I would like to use a beautiful image of a bunch of rose flowers. And the image credit goes to "mi9.com". You can get the image from this link : http://imgs.mi9.com/uploads/flower/4649/rose-flower-wallpaper-free_1920x1080_83181.jpg)

How do we do it ? We create a histogram of an image containing our object of interest (in our case, the rose flower, leaving leaves and background). The object should fill the image as far as possible for better results. And a color histogram is preferred over grayscale histogram, because color of the object is more better way to define the object than its grayscale intensity. ( A red rose flower and its green leaves may have same intensity in grayscale images, but easily distinguishable in color image). We then "back-project" this histogram over our test image where we need to find the object, ie in other words, we calculate the probability of every pixel belonging to rose flower and show it. The resulting output on proper thresholding gives us the rose flower alone.

So let's see how it is done.

Algorithm :

1 - First we need to calculate the color histogram of both the object we need to find (let it be 'M') and the image where we are going to search (let it be 'I').

`import cv2import numpy as npfrom matplotlib import pyplot as plt#roi is the object or region of object we need to findroi = cv2.imread('rose_red.png')hsv = cv2.cvtColor(roi,cv2.COLOR_BGR2HSV)#target is the image we search intarget = cv2.imread('rose.png')hsvt = cv2.cvtColor(target,cv2.COLOR_BGR2HSV)# Find the histograms. I used calcHist. It can be done with np.histogram2d alsoM = cv2.calcHist([hsv],[0, 1], None, [180, 256], [0, 180, 0, 256] )I = cv2.calcHist([hsvt],[0, 1], None, [180, 256], [0, 180, 0, 256] )`

2 - Find the ratio R = M/I

`R = M/(I+1)`

3 - Now backproject R, ie use R as palette and create a new image with every pixel as its corresponding probability of being target. ie B(x,y) = R[h(x,y),s(x,y)] where h is hue and s is saturation of the pixel at (x,y). After that apply the condition B(x,y) = min[B(x,y), 1].

`h,s,v = cv2.split(hsvt)B = R[h.ravel(),s.ravel()]B = np.minimum(B,1)B = B.reshape(hsvt.shape[:2])`

4 - Now apply a convolution with a circular disc, B = D * B, where D is the disc kernel.

`disc = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(5,5))cv2.filter2D(B,-1,disc,B)B = np.uint8(B)cv2.normalize(B,B,0,255,cv2.NORM_MINMAX)`

5 - Now the location of maximum intensity gives us the location of object. If we are expecting a region in the image, thresholding for a suitable value gives a nice result.

`ret,thresh = cv2.threshold(B,50,255,0)`

Below is one example I worked with. I used the region inside blue rectangle as sample object and I wanted to extract all the red roses. See, ROI is filled with red color only :

 Histogram Backprojection

Backprojection in OpenCV

OpenCV provides an inbuilt function cv2.calcBackProject(). Its parameters are almost same as the cv2.calcHist() function. One of its parameter is histogram which is histogram of the object and we have to find it. Also, the object histogram should be normalized before passing on to the backproject function. It returns the probability image. Then we convolve the image with a disc kernel and apply threshold. Below is my code and output :

`import cv2import numpy as nproi = cv2.imread('rose_green.png')hsv = cv2.cvtColor(img,cv2.COLOR_BGR2HSV)target = cv2.imread('rose.png')hsvt = cv2.cvtColor(target,cv2.COLOR_BGR2HSV)# calculating object histogramroihist = cv2.calcHist([hsv],[0, 1], None, [180, 256], [0, 180, 0, 256] )# normalize histogram and apply backprojectioncv2.normalize(roihist,roihist,0,255,cv2.NORM_MINMAX)dst = cv2.calcBackProject([hsvt],[0,1],roihist,[0,180,0,256],1)# Now convolute with circular discdisc = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(5,5))cv2.filter2D(dst,-1,disc,dst)# threshold and binary ANDret,thresh = cv2.threshold(dst,50,255,0)thresh = cv2.merge((thresh,thresh,thresh))res = cv2.bitwise_and(target,thresh)res = np.vstack((target,thresh,res))cv2.imwrite('res.jpg',res)`

Below is the output. Here ROI is not just flower, but some green part is also included. Still output is good. On close analysis of the center image, you can see the leaf parts slightly which will be removed on threshold :

 Histogram Backprojection in OpenCV

Summary

So we have looked on what is Histogram backprojection, how to calculate it, how it is useful in object detection etc. It is also used in more advanced object tracking methods like camshift. We will do that later.

Regards,
Abid Rahman K.

References :

1 - "Indexing via color histograms", Swain, Michael J. , Third international conference on computer vision,1990.
2 - http://www.codeproject.com/Articles/35895/Computer-Vision-Applications-with-C-Part-II
3 - http://theiszm.wordpress.com/tag/backprojection/

## Histograms - 3 : 2D Histograms

Hi friends,

In the first article, we calculated and plotted one-dimensional histogram. It is called one-dimensional because we are taking only one feature into our consideration, ie grayscale intensity value of the pixel. But in two-dimensional histograms, you consider two features. Normally it is used for finding color histograms where two features are Hue & Saturation values of every pixel.

There is a python sample in the official samples already for finding color histograms. We will try to understand how to create such a color histogram, and it will be useful in understanding further topics like Histogram Back-Projection.

2D Histogram in OpenCV

It is quite simple and calculated using the same function, cv2.calcHist(). For color histogram, we need to convert the image from BGR to HSV. (Remember, for 1D histogram, we converted from BGR to Grayscale). While calling calcHist(), parameters are :

channels = [0,1] # because we need to process both H and S plane.
bins = [180,256] # 180 for H plane and 256 for S plane
range = [0,180,0,256] # Hue value lies between 0 and 180 & Saturation lies between 0 and 256

`import cv2import numpy as npimg = cv2.imread('home.jpg')hsv = cv2.cvtColor(img,cv2.COLOR_BGR2HSV)hist = cv2.calcHist( [hsv], [0, 1], None, [180, 256], [0, 180, 0, 256] )`

That's it.

2D Histogram in Numpy

Numpy also provides a specific function for this : np.histogram2d(). (Remember, for 1D histogram we used np.histogram() ).

`import cv2import numpy as npfrom matplotlib import pyplot as pltimg = cv2.imread('home.jpg')hsv = cv2.cvtColor(img,cv2.COLOR_BGR2HSV)hist, xbins, ybins = np.histogram2d(h.ravel(),s.ravel(),[180,256],[[0,180],[0,256]])`

First argument is H plane, second one is the S plane, third is number of bins for each and fourth is their range.

Now we can check how to plot this color histogram

Plotting 2D Histogram

Method - 1 : Using cv2.imshow()
The result we get is a two dimensional array of size 180x256. So we can show them as we do normally, using cv2.imshow() function. It will be a grayscale image and it won't give much idea what colors are there, unless you know the Hue values of different colors.

Method - 2 : Using matplotlib
We can use matplotlib.pyplot.imshow() function to plot 2D histogram with different color maps. It gives us much more better idea about the different pixel density. But this also, doesn't gives us idea what color is there on a first look, unless you know the Hue values of different colors. Still I prefer this method. It is simple and better.

NB : While using this function, remember, interpolation flag should be 'nearest' for better results.

`import cv2import numpy as npfrom matplotlib import pyplot as pltimg = cv2.imread('home.jpg')hsv = cv2.cvtColor(img,cv2.COLOR_BGR2HSV)hist = cv2.calcHist( [hsv], [0, 1], None, [180, 256], [0, 180, 0, 256] )plt.imshow(hist,interpolation = 'nearest')plt.show()`

Below is the input image and its color histogram plot. X axis shows S values and Y axis shows Hue.

 2D Histogram in matplotlib with 'heat' color map

In histogram, you can see some high values near H = 100 and S = 200. It corresponds to blue of sky. Similarly another peak can be seen near H = 25 and S = 100. It corresponds to yellow of the palace. You can verify it with any image editing tools like GIMP.

Method 3 : OpenCV sample style !!
There is a sample code for color_histogram in OpenCV-Python2 samples. If you run the code, you can see the histogram shows even the corresponding color. Or simply it outputs a color coded histogram. Its result is very good (although you need to add extra bunch of lines).

In that code, the author created a color map in HSV. Then converted it into BGR. The resulting histogram image is multiplied with this color map. He also uses some preprocessing steps to remove small isolated pixels, resulting in a good histogram.

I leave it to the readers to run the code, analyze it and have your own hack arounds. Below is the output of that code for the same image as above:

 OpenCV-Python sample color_histogram.py output

You can clearly see in the histogram what colors are present, blue is there, yellow is there, and some white due to chessboard(it is part of that sample code) is there. Nice !!!

Summary :

So we have looked into what is 2D histogram, functions available in OpenCV and Numpy, how to plot it etc.

So this is it for today !!!

Regards,
Abid Rahman K.

## Histograms - 2 : Histogram Equalization

Hi friends,

In last article, we saw what is histogram and how to plot it. This time we can learn a method for image contrast adjustment called "Histogram Equalization".

So what is it ? Consider an image whose pixel values are confined to some specific range of values only. For eg, brighter image will have all pixels confined to high values. But a good image will have pixels from all regions of the image. So you need to stretch this histogram to either ends (as given in below image, from wikipedia) and that is what Histogram Equalization does (in simple words). This normally improves the contrast of the image.

 Histogram Equalization

Again, I would recommend you to read the wikipedia page on Histogram Equalization for more details about it. It has a very good explanation with worked out examples, so that you would understand almost everything after reading that. And make sure you have checked the small example given in "examples" section before going on to next paragraph.

So, assuming you have checked the wiki page, I will demonstrate a simple implementation of Histogram Equalization with Numpy. After that, I will present you OpenCV function. ( If you are not interested in implementation, you can skip this and go to the end of article)

Numpy Implementation

We start with plotting histogram and its cdf (cumulative distribution function) of the image in Wikipedia page. All the functions are known to us except np.cumsum(). It is used to find the cumulative sum (cdf) of a numpy array.

`import cv2import numpy as npfrom matplotlib import pyplot as pltimg = cv2.imread('wiki.jpg',0)hist,bins = np.histogram(img.flatten(),256,[0,256])cdf = hist.cumsum()cdf_normalized = cdf *hist.max()/ cdf.max() # this line not necessary.plt.plot(cdf_normalized, color = 'b')plt.hist(img.flatten(),256,[0,256], color = 'r')plt.xlim([0,256])plt.legend(('cdf','histogram'), loc = 'upper left')plt.show()`

 Input Image and its histogram

You can see histogram lies in brighter region. We need the full spectrum. For that, we need a transformation function which maps the input pixels in brighter region to output pixels in full region. That is what histogram equalization does.

Now we find the minimum histogram value (excluding 0) and apply the histogram equalization equation as given in wiki page. But I have used here, the masked array concept array from Numpy. For masked array, all operations are performed on non-masked elements. You can read more about it from Numpy docs on masked arrays

`cdf_m = np.ma.masked_equal(cdf,0)cdf_m = (cdf_m - cdf_m.min())*255/(cdf_m.max()-cdf_m.min())cdf = np.ma.filled(cdf_m,0).astype('uint8')`

Now we have the look-up table that gives us the information on what is the output pixel value for every input pixel value. So we just apply the transform.

`img2 = cdf[img]`

Now we calculate its histogram and cdf as before ( you do it) and result looks like below :

 Histogram Equalized Image and its histogram

You can see a better contrast in the new image, and it is clear from the histogram also. Also compare the cdfs of two images. First one has a steep slope, while second one is almost a straight line showing all pixels are equi-probable.

Another important feature is that, even if the image was a darker image (instead of a brighter one we used), after equalization we will get almost the same image as we got. As a result, this is used as a "reference tool" (I don't get a more suitable than this) to make all images with same light conditions. This is useful in many cases, for eg, in face recognition, before training the face data, the images of faces are histogram equalized to make them all with same light conditions. It provides better accuracy.

OpenCV Implementation

If you are bored of everything I have written above, just leave them. You need to remember only one function to do this, cv2.calcHist(). Its input is just grayscale image and output is our image.

Below is a simple code snippet showing its usage for same image we used :

`img = cv2.imread('wiki.jpg',0)equ = cv2.equalizeHist(img)res = np.hstack((img,equ)) #stacking images side-by-sidecv2.imwrite('res.png',res)`

See the result :

 OpenCV Histogram Equalization

So now you can take different images with different light conditions, equalize it and check the results.

Histogram equalization is good when histogram of the image is confined to a particular region. It won't work good in places where there is large intensity variations where histogram covers a large region, ie both bright and dark pixels are present. I would like to share to SOF questions with you. Please checkout the images in the questions, analyze their histograms, check resulting images after equalization :

How can I adjust contrast in OpenCV in C?
How do I equalize contrast & brightness of images using opencv?

So I would like to wind up this article here. In this article, we learned how to implement Histogram Equalization, how to use OpenCV for that etc. So take images, equalize it and have your own hack arounds.

See you next time !!!
Abid Rahman K.

## Histograms - 1 : Find, Plot, Analyze !!!

Hi,

This time, we will go through various functions in OpenCV related to histograms.

So what is histogram ? You can consider histogram as a graph or plot, which gives you an overall idea about the intensity distribution of an image. It is a plot with pixel values (ranging from 0 to 255) in X-axis and corresponding number of pixels in the image on Y-axis.

It is just another way of understanding the image. By looking at the histogram of an image, you get intuition about contrast, brightness, intensity distribution etc of that image. Almost all image processing tools today, provides features on histogram. Below is an image from "Cambridge in Color" website, and I recommend you to visit the site for more details.

 Image Histogram

You can see the image and its histogram. (Remember, this histogram is drawn for grayscale image, not color image). Left region of histogram shows the amount of darker pixels in image and right region shows the amount of brighter pixels. From the histogram, you can see dark region is more than brighter region, and amount of midtones (pixel values in mid-range, say around 127) are very less.

(For more basic details on histograms, visit : http://www.cambridgeincolour.com/tutorials/histograms1.htm)

FIND HISTOGRAM

Now we have an idea on what is histogram, we can look into how to find this. OpenCV comes with an in-built function for this, cv2.calcHist(). Before using that function, we need to understand some terminologies related with histograms.

BINS :
The above histogram shows the number of pixels for every pixel value, ie from 0 to 255. ie you need 256 values to show the above histogram. But consider, what if you need not find the number of pixels for all pixel values separately, but number of pixels in a interval of pixel values? say for example, you need to find the number of pixels lying between 0 to 15, then 16 to 31, ..., 240 to 255. You will need only 16 values to represent the histogram. And that is what is shown in example given in OpenCV Tutorials on histograms.

So what you do is simply split the whole histogram to 16 sub-parts and value of each sub-part is the sum of all pixel count in it. This each sub-part is called "BIN". In first case, number of bins where 256 (one for each pixel) while in second case, it is only 16. BINS is represented by the term "histSize" in OpenCV docs.

DIMS : It is the number of parameters for which we collect the data. In our case, we collect data regarding only one thing, intensity value. So here it is 1.

RANGE : It is the range of intensity values you want to measure. Normally, it is [0,256], ie all intensity values.

So now we use cv2.calcHist() function to find the histogram. Let's familiarize with the function and its parameters :
cv2.calcHist(images, channels, mask, histSize, ranges[, hist[, accumulate]])

1 - images : it is the source image of type uint8 or float32. it should be given in square brackets, ie, "[img]".
2 - channels : it is also given in square brackets. It the index of channel for which we calculate histogram. For example, if input is grayscale image, its value is [0]. For color image, you can pass [0],[1] or [2] to calculate histogram of blue,green or red channel respectively.
3 - mask : mask image. To find histogram of full image, it is given as "None". But if you want to find histogram of particular region of image, you have to create a mask image for that and give it as mask. (I will show an example later.)
4 - histSize : this represents our BIN count. Need to be given in square brackets. For full scale, we pass [256].
5 - ranges : this is our RANGE. Normally, it is [0,256].

So let's start with a sample image. Simply load an image in grayscale mode and find its full histogram.

`img = cv2.imread('home.jpg',0)hist = cv2.calcHist([img],[0],None,[256],[0,256])`

hist is a 256x1 array, each value corresponds to number of pixels in that image with its corresponding pixel value. Now we should plot it, but how ?

PLOTTING HISTOGRAM

There are two ways, 1) Short Way : use Matplotlib & 2) Long Way : use OpenCV functions

1 - Using Matplotlib:

Matplotlib comes with a histogram plotting function : matplotlib.pyplot.hist()

It directly finds the histogram and plot it. You need not use calcHist() function to find the histogram. See the code below:

`import cv2import numpy as npfrom matplotlib import pyplot as pltimg = cv2.imread('home.jpg',0)plt.hist(img.ravel(),256,[0,256]); plt.show()`

You will get a plot as below :

 Image Histogram

NOTE : Actually to find histogram, Numpy also provides you a function, np.histogram(). So instead of calcHist() function, you can try below line :

hist,bins = np.histogram(img,256,[0,256])

hist is same as we calculated before. But bins will have 257 elements, because numpy calculate bins as 0-0.99,1-1.99,2-2.99 etc. So final range would be 255-255.99. To represent that, they also add 256 at end of bins. But we don't need that 256. Upto 255 is sufficient.

Or you can use normal plot of matplotlib, which would be good for BGR plot. For that, you need to find the histogram data first. Try below code:

`import cv2import numpy as npfrom matplotlib import pyplot as pltimg = cv2.imread('home.jpg')color = ('b','g','r')for i,col in enumerate(color):    histr = cv2.calcHist([img],[i],None,[256],[0,256])    plt.plot(histr,color = col)    plt.xlim([0,256])plt.show()`

You will get a image as below :

 Histogram showing different channels

You can deduct from the above graph that, blue has some high value areas(obviously it should be the due to sky)

2 - Using OpenCV functions :

Well, here you adjust the values of histograms along with its bin values to look like x,y coordinates so that you can draw it using cv2.line() or cv2.polyline() function to generate same image as above. This is already available with OpenCV-Python2 official samples. You can check that : https://github.com/Itseez/opencv/blob/master/samples/python2/hist.py . I had already mentioned it in one of my very early articles : Drawing Histogram in OpenCV-Python

Now we used calcHist to find the histogram of full image. What if you want to find some regions of an image? Just create a mask image with white color on the region you want to find histogram and black otherwise. I have demonstrated it while answering a SOF question. So I would like you to read that answer (http://stackoverflow.com/a/11163952/1134940). Just for a demo, I provide the same images here :

Due to resizing, histogram plot clarity is reduced. But I hope you can write your own code and analyze it.

SUMMARY
In short, we have seen what is image histogram, how to find and interpret histograms, how to plot histograms etc. It is sufficient for today. We will look into other histogram functions in coming articles.

Hope you enjoyed it !!! Feel free to share !!!

Abid Rahman K.

## Contours - 5 : Hierarchy

Hi,

In the last few articles on contours, you have worked with several functions related to contours provided by OpenCV. But when we found the contours in image using cv2.findContours() function, we have passed two arguments additional to source image. They are Contour Retrieval Mode and Contour Approximation Method. We usually passed cv2.RETR_LIST or cv2.RETR_TREE for first argument and cv2.CHAIN_APPROXIMATE_SIMPLE for second argument, and they worked nice. But what do they actually mean ?

Also, in the output, we got two arrays, one is our contours, and one more output which we named as 'hierarchy' (Please checkout the codes in previous articles). But we never used this hierarchy anywhere. Then what is this hierarchy and what is it for ? What is its relationship with the previous mentioned function arguments ?

I don't know how important is this topic. Mainly because, I have never worried about hierarchy and other arguments in any of my projects. And there was no reason to. But I am sure, there might be some people who benefit from these features, otherwise OpenCV devs wouldn't have spent time to introduce such a feature. So whatever may be its use, let's just go through it. :)

So, what is this "hierarchy" ?

Normally we use the findContours() function to detect objects in an image, right ? Sometimes objects are in different locations. But in some cases, some shapes are inside other shapes. Just like nested figures. In this case, we call outer one as parent and inner one as child. This way, contours in an image has some relationship to each other. And we can specify how one contour is connected to each other, like, is it child of some other contour, or is it a parent etc. Representation of this relationship is called the hierarchy.

Consider an example image below :

 Hierarchy Representation

In this image, there are a few shapes which I have numbered from 0 to 5. 2 and 2a denotes the external and internal contour of the outermost box..

Here, contours 0,1,2 are external or outermost. We can say, they are in hierarchy-0 or simply they are in same hierarchy level.

Next comes contour 2a. It can be considered as a child of contour 2 (or in opposite way, contour 2 is parent of contour 2a). So let it be in hierarchy-1. Similarly contour 3 is child of contour 2 and it comes in next hierarchy. Finally contours 4,5 are the children of 3a, and they come in the last hierarchy level. From the way I numbered the boxes, I would say contour 4 is the first child of contour 3a.

I mentioned these things to understand terms like "same hierarchy level", "external contour", "child contour", "parent contour", "first child" etc. Now let's get into OpenCV.

Hierarchy Representation in OpenCV :

So each contour has its own information regarding what hierarchy it is, who is its child, who is its parent etc. OpenCV represents it as an array of four values : [Next, Previous, First_Child, Parent]
"Next denotes next contour at the same hierarchical level."
For eg, take contour 0 in our picture. Who is next contour in its same level ? It is contour 1. So simply put it as 1. Similarly for Contour 1, next is contour 2. So Next = 2.

What about contour 2? There is no next contour in same level. So simply, put it as -1.

What about contour 4? It is in same level with contour 5. So its next contour is contour 5.
"Previous denotes previous contour at the same hierarchical level."
It is same as above. Previous contour of contour 1 is contour 0 in same level. Similarly for contour 2, it is contour 1. And for contour 0, there is no previous, so put it as -1.
"First_Child denotes its first child contour."
I think there is no need of any explanation. For contour 2, child is contour 2a. So it gets the corresponding index value of contour 2a.

What about contour 3a? It has two children. But we take only first child. And it is contour 4. So First_Child = 4 for contour 3a.
"Parent denotes index of its parent contour"
It is just opposite of First_Child. Both for contour 4 and 5, parent contour is contour 3a. For 3a, it is contour 3 and so on.

If there is no child or parent, that field is taken as -1.

So now we know about the hierarchy style used in OpenCV, we can check into Contour Retrieval Modes in OpenCV with the help of same image given above. ie what do flags like cv2.RETR_LIST, cv2.RETR_TREE, cv2.CCOMP, cv2.EXTERNAL etc mean?

Contour Retrieval Mode :

This is the second argument in cv2.findContours() function. Lets' understand each flag one-by-one.

cv2.RETR_LIST :

This is the simplest of the four flags (from explanation point of view). It simply retrieves all the contours, but doesn't create any parent-child relationship. "Parents are kids are equal under this rule, and they are just contours". ie they all belongs to same hierarchy level.

So here, 3rd and 4th term in hierarchy array is always -1. But obviously, Next and Previous terms will have their corresponding values. Just check it yourself and verify it.

Below is the result I got, and each row is hierarchy details of corresponding contour. For eg, first row corresponds to contour 0. Next contour is contour 1. So Next = 1. There is no previous contour, so Previous = 0. And the remaining two, as told before, it is -1.

`>>> hierarchyarray([[[ 1, -1, -1, -1],        [ 2,  0, -1, -1],        [ 3,  1, -1, -1],        [ 4,  2, -1, -1],        [ 5,  3, -1, -1],        [ 6,  4, -1, -1],        [ 7,  5, -1, -1],        [-1,  6, -1, -1]]])`

This is the good choice to use in your code, if you are not using any hierarchy features.

cv2.RETR_EXTERNAL

If you use this flag, it returns only extreme outer flags. All child contours are left behind. "We can say, under this law, Only the eldest in every family is taken care of. It doesn't care about other members of the family :)".

So, in our image, how many extreme outer contours are there? ie at hierarchy-0 level?. Only 3, ie contours 0,1,2, right? Now try to find the contours using this flag. Here also, values given to each element is same as above. Compare it with above result. Below is what I got :
`>>> hierarchyarray([[[ 1, -1, -1, -1],        [ 2,  0, -1, -1],        [-1,  1, -1, -1]]])`

You can use this flag if you want to extract only the outer contours. It might be useful in some cases.

cv2.RETR_CCOMP :

This flag retrieves all the contours and arranges them to a 2-level hierarchy. ie external contours of the object (ie its boundary) are placed in hierarchy-1. And the contours of holes inside object (if any) is placed in hierarchy-2. If any object inside it, its contour is placed again in hierarchy-1 only. And its hole in hierarchy-2 and so on.

Just consider the image of a "big white zero" on a black background. Outer circle of zero belongs to first hierarchy, and inner circle of zero belongs to second hierarchy.

We can explain it with a simple image. Here I have labelled the order of contours in red color and the hierarchy they belongs to, in green color (either 1 or 2). The order is same as the order OpenCV detects contours.

So consider first contour, ie contour-0. It is hierarchy-1. It has two holes, contours 1&2, and they belong to hierarchy-2. So for contour-0, Next contour in same hierarchy level is contour-3. And there is no previous one. And its first is child is contour-1 in hierarchy-2. It has no parent, because it is in hierarchy-1. So its hierarchy array is [3,-1,1,-1]

Now take contour-1. It is in hierarchy-2. Next one in same hierarchy (under the parenthood of contour-1) is contour-2. No previous one. No child, but parent is contour-0. So array is [2,-1,-1,0].

Similarly contour-2 : It is in hierarchy-2. There is not next contour in same hierarchy under contour-0. So no Next. Previous is contour-1. No child, parent is contour-0. So array is [-1,1,-1,0].

Contour - 3 : Next in hierarchy-1 is contour-5. Previous is contour-0. Child is contour-4 and no parent. So array is [5,0,4,-1].

Contour - 4 : It is in hierarchy 2 under contour-3 and it has no sibling. So no next, no previous, no child, parent is contour-3. So array is [-1,-1,-1,3].

Remaining you can fill up. This is the final answer I got:

`>>> hierarchyarray([[[ 3, -1,  1, -1],        [ 2, -1, -1,  0],        [-1,  1, -1,  0],        [ 5,  0,  4, -1],        [-1, -1, -1,  3],        [ 7,  3,  6, -1],        [-1, -1, -1,  5],        [ 8,  5, -1, -1],        [-1,  7, -1, -1]]])`

So where do we can apply this ? I don't have any good application now. One application would be in OCR. Those who have checked my article "Simple Digit Recognition OCR in OpenCV-Python" would have noticed that I used area as a constraint to remove the contours of holes inside numbers like 8,9,0,6 etc. I found that area by checking a lot of values. Instead, I should have used this feature to filter out holes inside the numbers.(To be honest, I had no idea regarding the hierarchy when I wrote that code.)

UPDATE : You can find a simple demo of practical application of cv2.RETR_CCOMP in this SOF link : http://stackoverflow.com/a/14279746/1134940

cv2.RETR_TREE :

And this is the final guy, Mr.Perfect. It retrieves all the contours and creates a full family hierarchy list. "It even tells, who is the grandpa, father, son, grandson and even beyond... ".

For examle, I take above image, rewrite the code for cv2.RETR_TREE, reorder the contours as per the result given by OpenCV and analyze it. Again, red letters give the contour number and green letters give the hierarchy order.

Take contour-0 : It is in hierarchy-0. Next contour in same hierarchy is contour-7. No previous contours. Child is contour-1. And no parent. So array is [7,-1,1,-1].

Take contour-2 : It is in hierarchy-1. No contour in same level. No previous one. Child is contour-2. Parent is contour-0. So array is [-1,-1,2,0].

And remaining, try yourself. Below is the full answer:

`>>> hierarchyarray([[[ 7, -1,  1, -1],        [-1, -1,  2,  0],        [-1, -1,  3,  1],        [-1, -1,  4,  2],        [-1, -1,  5,  3],        [ 6, -1, -1,  4],        [-1,  5, -1,  4],        [ 8,  0, -1, -1],        [-1,  7, -1, -1]]])`

I am not sure where you can use it.

So this is what Contour Retrieval Mode.

Next we will deal with third argument in cv2.findContours(), ie Contour Approximation method.

Contour Approximation Method

There are 3 flags under this category, but I am discussing only the first two - cv2.CHAIN_APPROX_NONE and cv2.CHAIN_APPROX_SIMPLE.

First one finds all the points on the contour or the boundary. But actually do we need all the points? For eg, you found the contour of a straight line. Do you need all the points on the line to represent that line? No, we need just two end points of that line. This is what second flag does. It removes all redundant points and compresses the contour.

It can be easily visualized as follows. Take an image with upright rectangle in it. Find the contours using both the flags (Take second argument as cv2.RETR_LIST). First compare number of points in each contour. Now plot each point in both the contour on the rectangle and compare the result. See it below :

 contours using cv2.CHAIN_APPROX_SIMPLE

 contours using cv2.CHAIN_APPROX_NONE

In first case, you can see a blue boundary. It is because, all the points plotted are touching each other. Actually they are distinct points. And it has 734 points in the array. But second method has only four points in four corners. That is really a good difference. Second method is a good improvement, both in memory consumption and performance.

**********************************************************************************

So I think you might have got a simple intuitive understanding regarding concept of hierarchy in OpenCV. As I mentioned in the beginning of this article, I don't know how important is this topic, since I have never used this. If I find any application using this hierarchy, I will provide the links here.

Regards,

Abid Rahman K.

Previous Articles on Contours :

## K-Means Clustering - 2 : Working with Scipy

Hi,

In the previous article, 'K-Means Clustering - 1 : Basic Understanding', we understood what is K-Means clustering, how it works etc. In this article, we will use k-means functionality in Scipy for data clustering. OpenCV will be covered in another article.

Scipy's cluster module provides routines for clustering. The vq module in it provides k-means functionality. You will need Scipy version 0.11 to get this feature.

We also use Matplotlib to visualize the data.

Note : All the data arrays used in this article are stored in github repo for you to check. It would be nice to check it for a better understanding. It is optional. Or you can create your own data and check it.

So we start by importing all the necessary libraries.

`>>> import numpy as np>>> from scipy.cluster import vq>>> from matplotlib import pyplot as plt`

Here I would like to show three examples.

1 - Data with only one feature :

Consider, you have a set of data with only one feature, ie one-dimensional. For eg, we can take our t-shirt problem where you use only height of people to decide the size of t-shirt.

Or, from an image processing point of view, you have a grayscale image with pixel values ranges from 0 to 255. You need to group it into just two colors, may be black and white only. ( That is another version of thresholding. I don't think someone will use k-means for thresholding. So just take this as a demo of k-means.)

So we start by creating data.

`>>> x = np.random.randint(25,100,25)>>> y = np.random.randint(175,255,25)>>> z = np.hstack((x,y))>>> z = z.reshape((50,1))`

So we have 'z' which is an array of size 50, and values ranging from 0 to 255. I have reshaped 'z' to a column vector. It is not necessary here, but it is a good practice. Reason, I will explain in coming sections. Now we can plot this using Matplotlib's histogram plot.

`>>> plt.hist(z,256,[0,256]),plt.show()`

We get following image :

 Test Data

Now we use our k-means functions.

First function, vq.kmeans(), is used to cluster the data as per our requirements and it returns the centroids of the clusters. (Docs)

It takes our test data and number of clusters we need as inputs. Other two inputs are optional and is not of big concern now.

`>>> centers,dist = vq.kmeans(z,2)>>> centersarray([[207],       [ 60]])`

First output is 'centers', which are the centroids of clustered data. For our data, it is 60 and 207. Second output is the distortion between centroids and test data. We mark the centroids along with the inputs.

`>>> plt.hist(z,256,[0,256]),plt.hist(centers,32,[0,256]),plt.show()`

Below is the output we got. Those green bars are the centroids.

 Green bars shows centroids after clustering

Now we have found the centroids. From first article, you might have seen our next job is to label the data '0' and '1' according to distance to the centroids. We use vq.vq() function for this purpose.

vq.vq() takes our test data and centroids as inputs and provides us the labelled data,called 'code' and distance between each data and corresponding centroids.

`>>> code, distance = vq.vq(z,centers)`

If you compare the arrays 'code' and 'z' in git repo, you can see all values near to first centroid will be labelled '0' and next as '1'.

Also check the distance array. 'z[0]' is 47, which is near to 60, so labelled as '1' in 'code'. And distance between them is 13, which is 'distance[0]'. Similarly you can check other data also.

Now we have the labels of all data, we can separate the data according to labels.

`>>> a = z[code==0]>>> b = z[code==1]`

'a' corresponds to data with centroid = 207 and 'b' corresponds to remaining data. (Check git repo to see a&b).

Now we plot 'a' in red color, 'b' in blue color and 'centers' in yellow color as below:

`>>> plt.hist(a,256,[0,256],color = 'r') # draw 'a' in red color>>> plt.hist(b,256,[0,256],color = 'b') # draw 'b' in blue color>>> plt.hist(centers,32,[0,256],color = 'y') # draw 'centers' in yellow color>>> plt.show()`

We get the output as follows, which is our clustered data :

 Output of K-Means clustering

So, we have done a very simple and basic example on k-means clustering. Next one, we will try with more than one features.

2 - Data with more than one feature :

In previous example, we took only height for t-shirt problem. Here, we will take both height and weight, ie two features.

Remember, in previous case, we made our data to a single column vector. This is because, it is a good convention, and normally followed by people from all fields. ie each feature is arranged in a column, while each row corresponds to an input sample.

For example, in this case, we set a test data of size 50x2, which are heights and weights of 50 people. First column corresponds to height of all the 50 people and second column corresponds to their weights. First row contains two elements where first one is the height of first person and second one his weight. Similarly remaining rows corresponds to heights and weights of other people. Check image below:

So now we can prepare the data.

`>>> x = np.random.randint(25,50,(25,2))>>> y = np.random.randint(60,85,(25,2))>>> z = np.vstack((x,y))`

Now we got a 50x2 array. We plot it with 'Height' in X-axis and 'Weight' in Y-axis.

`>>> plt.scatter(z[:,0],z[:,1]),plt.xlabel('Height'),plt.ylabel('Weight')>>> plt.show()`

(Some data may seem ridiculous. Never mind it, it is just a demo)

 Test Data

Now we apply k-means algorithm and label the data.

`>>> center,dist = vq.kmeans(z,2)>>> code,distance = vq.vq(z,center)`

This time, 'center' is a 2x2 array, first column corresponds to centroids of height, and second column corresponds to centroids of weight.(Check git repo data)

As usual, we extract data with label '0', mark it with blue, then data with label '1', mark it with red, mark centroids in yellow and check how it looks like.

`>>> a = z[code==0]>>> b = z[code==1]>>> plt.scatter(a[:,0],a[:,1]),plt.xlabel('Height'),plt.ylabel('Weight')>>> plt.scatter(b[:,0],b[:,1],c = 'r')>>> plt.scatter(center[:,0],center[:,1],s = 80,c = 'y', marker = 's')>>> plt.show()`

This is the output we got :

 Result of K-Means clustering

So this is how we apply k-means clustering with more than one feature.

Now we go for a simple application of k-means clustering, ie color quantization.

3 - Color Quantization :

Color Quantization is the process of reducing number of colors in an image. One reason to do so is to reduce the memory. Sometimes, some devices may have limitation such that it can produce only limited number of colors. In those cases also, color quantization is performed.

There are lot of algorithms for color quantization. Wikipedia page for color quantization gives a lot of details and references to it. Here we use k-means clustering for color quantization.

There is nothing new to be explained here. There are 3 features, say, R,G,B. So we need to reshape the image to an array of Mx3 size (M is just a number). And after the clustering, we apply centroid values (it is also R,G,B) to all pixels, such that resulting image will have specified number of colors. And again we need to reshape it back to the shape of original image. Below is the code:

`import cv2import numpy as npfrom scipy.cluster import vqimg = cv2.imread('home.jpg')z = img.reshape((-1,3))k = 2           # Number of clusterscenter,dist = vq.kmeans(z,k)code,distance = vq.vq(z,center)res = center[code]res2 = res.reshape((img.shape))cv2.imshow('res2',res2)cv2.waitKey(0)cv2.destroyAllWindows()`

Change the value of 'k' to get different number of colors. Below is the original image and results I got for values k=2,4,8 :

 Color Quantization with K-Means clustering

So, that's it !!!

In this article, we have seen how to use k-means algorithm with the help of Scipy functions. We also did 3 examples with sufficient number of images and plots. There are two more functions related to it, but I will deal it later.

In next article, we will deal with OpenCV k-means implementation.

I hope you enjoyed it...

Regards,

Abid Rahman K.

Ref :

1 - Scipy cluster module documentation

2 - Color Quantization

## K-Means Clustering - 1 : Basic Understanding

Hi,

In this section, we will be dealing with K-Means clustering, a machine learning algorithm, which is used for grouping a large set of data to desired number of groups depending on their similarity. It will be a series of articles, may be two or three articles.

In this article, we mainly focus on the understanding what is this algorithm, how it works, what are its applications etc. I think an intuitive understanding is more better than explaining the mathematical background behind the algorithm.

In the coming articles, I will explain how to use in-built functions of Scipy and OpenCV for K-Means clustering.

(Note : All images are sufficiently larger, but resized to fit in page. Just click on the image to see it in its original size)

By the way, What is this algorithm for ?

According to Wikipedia :

k-means clustering is a method of cluster analysis which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean.

( Reading above passage, I hope you might have understood at-least this : It groups large data to some groups based on some features.)

If you didn't understand above statements, I will tell a couple of examples :

I am sure you will have visited Google News at-least once. For every news, Google provides a main article and just below it, there are links to corresponding news from all other newspapers. Check below image :

This is one of my favorite features in Google News, because I try to read news on same topic from different papers. (It helps me to understand how media play with our minds. Different newspapers try to present same news in different ways to audience. And it is seen frequently with respect to political news and people reading them are, most often, got biased by these news, while real truth is hidden from them. Presently the power of media is such that, if you control the media, you control the world. Anyway, it is out of our topic. )

I have always wondered how does Google achieve this. I am not claiming Google uses k-means clustering, but this is what K-Means clustering also does, You have a large set of news and group them according to its content.

2 - T-shirt size problem

This example is commonly used to explain clustering problems.

Consider a company, which is going to release a new model of T-shirt to market. Obviously they will have to manufacture models in different sizes to satisfy people of all sizes. So the company make a data of people's height and weight, and plot them on to a graph, as below:

 People Height v/s Weight plot

Company can't create t-shirts with all the sizes. Instead, they divide people to Small, Medium and Large, and manufacture only these 3 models which will fit into all the people. This grouping of people into three groups can be done by k-means clustering, and algorithm provides us best 3 sizes, which will satisfy all the people. And if it doesn't, company can divide people to more groups, may be five, and so on. Check image below :

 People grouped to different clusters

So, now I hope, you might have understood use of this algorithm. Now we can go to next step.

How does the algorithm work ?

This algorithm is an iterative process. We will explain it step-by-step with the help of images.

Consider a set of data as below ( Don't be bothered about what this data is, or you can consider it as t-shirt problem). We need to cluster this data into two groups.

 Test Data

Step :1 - Algorithm randomly chooses two centroids, c1 and c2 (sometimes, any two data are taken as the centroids).

Step :2 - Then it calculates the distance from each point to both centroids. If a test data is more closer to c1, then that data is labelled with '0'. If it is closer to c2, then labelled as '1' (If more centroids are there, labelled as '2','3' etc).

In our case, we will color all '0' labelled with red, and '1' labelled with blue. So we get following image after above operations.

 Initial centroid selection and data labelling

Step :3 - Next we calculate the average of all blue points and red points separately and that will be our new centroids. That is c1 and c2 shift to newly calculated centroids. (Remember, the images shown are not true values and not to true scale, it is just for demonstration only. So calculated averages may not be what you expect).

And again, perform step 2 with new centroids and label data to '0' and '1'.

So we get result as below :

 New centroid calculated and data re-labelled

Now step - 2 and step - 3 are iterated until both centroids are converged to fixed points. These points are such that sum of distances between test data and their corresponding centroids are minimum. Or simply, sum of distances between red data & c1 and blue data & c2 is minimum.

Final result almost looks like below :

 Final Result

So, I hope by this time, you would have obtained a basic understanding how K-Means clustering works. With this intuitive knowledge, read some good text books to understand the mathematics behind this algorithm. I am sure you won't find any difficulty to understand it.

It is just a top layer of K-Means clustering. There are a lot of modifications to this algorithm like, how to choose the initial centroids, how to speed up the iteration process etc. Me too, haven't gone much deeper and I think this would be sufficient to start working with K-Means clustering. Those who need more knowledge can read any good text books.

So that was a complete theoretical, easy-to-read article.

In next article, we will see how to use Scipy's kmeans implementation for data clustering, and we will deal OpenCV implementation in later article.

So that's all for now.

Regards,

Abid Rahman K.

Ref :

1 - Stanford Machine Learning classes by Prof. Andrew Ng

## SOF : Watershed in OpenCV

Hi,

Do you like to have a very simple example for watershed algorithm in OpenCV ?

Please visit : Watershed in OpenCV-Python

See the demo result below :

 Original Image
 Foreground extracted using watershed.

With Regards,

ARK.

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